Use an off-the-shelf signal source as a jitter/wander generator
Edited by Brad Thompson
Slobodan Milijevic, Zarlink Semiconductor -- EDN, February 3, 2005
Ensuring that new networked products, such as routers, gateways or DSLAMs (digital-subscriber-line- access multiplexers) meet stringent timing specifications usually requires a specialized jitter/wander generator. As a substitute, you can use a standard function generator equipped with PM (phase modulation) or FM (frequency modulation) to measure jitter and wander tolerance. This Design Idea describes how to convert PM and FM parameters (phase deviation, frequency deviation, and modulating frequency) into jitter/wander parameters—amplitude in UIs (unit intervals) and frequency.
Network-communications engineers use the terms "jitter" and "wander" to describe phase noise in digital signals. "Wander" refers to phase noise at frequencies below 10 Hz, and "jitter" refers to phase noise at frequencies at or above 10 Hz. Defining phase noise requires specifying both its amplitude and its frequency.
As Figure 1 shows, if you observe a clock with phase noise on an oscilloscope triggered by a clock of the same frequency but without phase noise, the rising and falling edges of the noisy clock appear blurred—that is, not clearly defined in time. If the clock has low frequency-phase noise (wander), the rising and falling edges move back and forth at a rate equal to the wander frequency. The range of this movement defines the jitter/wander amplitude.
Figure 2 illustrates an instance of sine-wave-shaped FM of jitter or wander. You can express jitter or wander amplitude in UIs; one UI is equal to the clock period. For example, the amplitude of the jitter/wander in Figure 2 is 0.25 UI p-p.
You can use a signal generator to generate waveform jitter and wander by connecting a low-frequency signal source to the signal generator's PM or FM input. Equation 1 applies to both FM and PM and describes the general form of an angle-modulating signal:
s(t)=Acos[2πfCt+θ(t)]. EQUATION 1
Although in digital communications, s(t) usually approximates a square-wave function, using a square wave instead of a sine wave complicates the math but doesn't affect the process of angle modulation. For simplicity, this Design Idea uses a sine-wave function for s(t).
For PM, the phase θ(t) in Equation 1 is proportional to the modulation signal:
θ(t)=DPMcos(2πfmt), EQUATION 2
where DPM is the phase deviation (peak variation of the phase), and fm represents the modulating frequency, which is also the jitter/wander frequency. The relationship between phase deviation and jitter/wander amplitude is straightforward, and you can obtain it from:
JITTER/WANDER[UI p-p]=DPM/180°, EQUATION 3
where DPM has units of radians in communications theory, but, for convenience, most signal generators specify units of degrees instead.
For FM, the phase θ(t) in Equation 1 is proportional to the integral of modulating signal.
EQUATION 4
where DFM is the frequency deviation (peak variation of the frequency) and fm is the modulating frequency. The FM modulating frequency is the same as the jitter/wander frequency. Equation 5 yields the jitter/wander amplitude:
EQUATION 5
which derives from Equation 6:
EQUATION 6
Therefore, the peak-to-peak deviation of θ(t) is:
EQUATION 7
in which the factor of 2 originates from the peak-to-peak amplitude of a sine-wave function. To get jitter/wander in peak-to-peak unit intervals, divide Equation 7 by the period of the sine-wave function, 2π. Thus, you get Equation 6, which is valid only when the modulating signal comprises a sine wave because the integral of a sine wave is also a sine-wave function shifted in phase. Fortunately, most jitter/wander-tolerance tests almost exclusively use sine-wave modulation.
Some signal generators specify modulation in phase and frequency span instead of phase and frequency deviation. For PM, the span is the peak-to-peak variation of the phase, and, for FM, the span is the peak-to-peak variation of the frequency. That is, the span equals twice the deviation for both PM and FM. In this case, the jitter/wander amplitude for PM is:
EQUATION 8
and it is:
EQUATION 9
for FM.
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